Ferromagnetic to paramagnetic transition in spherical spin glass

Abstract

We consider the spherical spin glass model defined by a combination of the pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian and the ferromagnetic Curie-Weiss Hamiltonian. In the large system limit, there is a two-dimensional phase diagram with respect to the temperature and the coupling strength. The phase diagram is divided into three regimes; ferromagnetic, paramagnetic, and spin glass regimes. The fluctuations of the free energy are known in each regime. In this paper, we study the transition between the ferromagnetic regime and the paramagnetic regime in a critical scale.

arXiv comment41pages, 2 figures

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Cited by in corpus (16)

• Spherical spin glass model with external field
• Central limit theorem near the critical temperature for the overlap in the 2-spin spherical SK model
• The number of saddles of the spherical $p$-spin model
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Free energy fluctuations of the $2$-spin spherical SK model at critical temperature
• Fluctuation of the free energy of Sherrington-Kirkpatrick model with Curie-Weiss interaction: the paramagnetic regime
• Weak detection in the spiked Wigner model
• Spherical Integrals of Sublinear Rank
• Infinite volume Gibbs states and metastates of the random field mean-field spherical model
• Overlap of a spherical spin glass model with microscopic external field
• Mean Field Spin Glass Models under Weak External Field
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction
• Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
• Local law and Tracy--Widom limit for sparse stochastic block models
• CLT for LSS of sample covariance matrices with unbounded dispersions
• Generalised Gibbs Ensemble for spherically constrained harmonic models